On nonsystematic perfect codes over finite fields
S. A. Malyugin · Journal of Applied and Industrial Mathematics · 2010
The nonsystematic perfect q-ary codes over finite field F q of length n = (q m − 1)/(q − 1) are constructed in the case when m ≥ 4 and q ≥ 2 and also when m = 3 and q is not prime. For q ≠ 3, 5, these codes can be constructed by switching seven disjoint components of the Hamming code H ; and, for q = 3, 5, eight disjoint components.